What are the most challenging tasks aiming to achieve the lowest error rate?
Yes. Here are some of the most prominent ones and their respective state-of-the-art errors:


CIFAR-10: ~3.5% error
CIFAR-100: ~24% error  
STL-10: ~26% error
SVHN: ~1.7% error
ImageNet tasks: the best 2012 classification task solution got 15% top-5 error, better results are currently available


You can check an updated list of solutions here. Also, a more comprehensive list of modern datasets can be found here.